That being said, giving more agency to the players isn't necessarily the answer. Obviously, take too much away and it stops being interactive, but give too much and you have to hope that a narrative emerges. ("The Sims" is a perfect example of near-total player agency — stories will often result from playing The Sims, but they're often player-generated and player-detailed. In other words, the players create the structure, not the authors of the game, a power balance that's closer to an RPG designer and a play group than a traditional video game team and its customers.) Again, giving the players the chance to create their own stories is powerful, but the idea of this is to balance author and player agency in a way that is recognizable as the same "story" between individuals.

I talk about story in one of my ICC presentations (I forget which one — check the "Free Stuff" page to reference them). There, I mention something that was the germ of this opinion — that "story" comes after interactions. You play the game, and then afterwards you piece it together into a story. More work at the onset makes it easier to draw a logical narrative, but even totally random games can have some kind of narrative once it's experiences. LARPs are unique because dozens or hundreds of people are involved in the same suite of interactions (not the exact same interactions, but a limited set of them) and get a variety of similar-but-unique stories from it. The further removes the players are from the main action, the more their story differs from the rest of the group, and it's even possible for regularly marginalized players to end up playing a subtly different game entirely over time.

Coming around to your question (finally!), yes I believe blobs are best designed when they are linked together into an implied story to start. Players will naturally follow the narrative intent of the blobs, but with enough flex between them, they will find unique stories of their own. I think the Grand Theft Auto games do this really well — there's a clear story over the course of the various missions, but how you get from mission to mission, and sometimes how you complete each mission, is up to each individual player.

Footnote 1: In case it isn't clear, "agency" in this case means "narrative authority," or who drives the pace and progress of the story.

For example, the new Adventure Path over at Paizo creates a whole section of the world that you and your group are thrust into with a goal in mind – there are points of interest, but the whole thing is up to the players. I've done this in LARP as well (with mixed success).

I guess the question is: do blobs of story or blobs of interactive area do better when trying to tell an emergent story?